How to compute a value in 100 years if it grows at rate g


1. Here we'll take a look at government debt. Say that a country had government debt of $1,000 billion at the end of 2016 and during 2017 they ran a surplus of $200 billion (i.e., that tax collections were $200 billion more than government's spending). At the end of 2017 the total amount the government owed would be ___. In addition, this would most likely be influenced by ___.

a. $200 billion, the President and Congress
b. $800 billion, the President and Congress
c. $1,000 billion, the President and Congress
d. $1,200 billion, the President and Congress
e. $200 billion, the Fed
f. $800 billion, the Fed
g. $1,000 billion, the Fed
h. $1,200 billion, the Fed

2. We sometimes compute %Δnominal price - %ΔCPI. Which of the following are times when we do? More than one of the following might be correct.

a.When computing real GDP
b.When computing economic growth at an annual rate.
c.When computing nominal GDP.
d.When computing the inflation rate (recall it is at an annual rate)
e.When computing the change in a real price.
f.When computing Total Factor Productivity ("A" in the per-worker production function).
g.When putting a price from one year in terms of prices in another year.
h.When computing labor productivity.
i.When computing real per capita GDP.

3. Let's say that country A's rate of growth is 2% and country B's is 2.2%. Both now have per capita real GDP of $20,000. Compute their per capita real GDP 100 years in the future given these growth rates. Which concept does your answer illustrate? Hint: on how to compute a value in 100 years if it grows at rate g, you can solve our growth rate formula for the final value of the variable. That is, solve g = (final value / initial value) (1/n) - 1 for final value.

a. the rule of 70
b.diminishing returns in the production process
c.technology (as economists define the term)
d.economic growth is zero-sum
e.small differences in growth rates matter over many years

4. Say that over the last 25 years you see an economy where a steadily growing portion of the population is working (from 45% of the population to 55%), prices have been rising by 1.5% a year, total factor productivity (TFP, which measures A in the per-worker production function) went from 2,000 to 3,000, and the amount of capital per worker rose from $50,000 to $75,000. What would most likely be happening to real per capita GDP over these 25 years?

a.growing
b.staying the same
c. falling

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Macroeconomics: How to compute a value in 100 years if it grows at rate g
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